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USGS2025

The effects of line simplification on planform geometry

Data on maps should retain accuracy regardless of scale. Yet, as cartographic lines are generalized, there can be impacts on properties such as topology, density, and planform geometry. Here, we investigate the use of the Scale Specific Sinuosity (S3) metric (Stanislawski et al., 2023) to evaluate the effects of line simplification on planform geometry, which is the bends of streams in map view. We employ an open-source Python S3 workflow to characterize the geometry of five diverse stream channels in the United States. The original data are extracted from the U.S. Geological Survey National Hydrography Dataset 1:24,000-scale vector data (U.S. Geological Survey, 2000) (Table 1), and the simplification is done using the Visvalingam and Whyatt method (2017) with a simplification tolerance of 0.5, 1.0, 1.5, and 2.0 km. The S3 analysis is calculated at each level of simplification and S3 derivatives are generated. Derivatives include measures of sinuosity, fractal dimension, and the dominant bend wavelength. The findings show that the change in planform geometry is scale-dependent, though simplification will have little effect on straighter lines. The change becomes more apparent in complex lines as the degree of simplification aligns with the scale of the dominant bend geometries. These logical conclusions are evidence that the S3 is a useful metric for automated characterization of bend geometry regardless of line complexity.

Conference Paper↗

USGS1992

Remote sensing studies of the geomorphology of Surtsey, 1987-1991

The volcanic island of Surtsey, formed by explosive submarine and effusive subaerial eruptions between November 1963 and June 1967, consists of a complex combination of primary and redeposited tephra and alkaline olivine basalt lava flows in a 2.5 km 2 area (Thorarinsson, 1967; Thorarinsson et al., 1964; Fridriksson, 1975). During the past 24 years, wave and wind erosion of this subaerial mid-ocean ridge (MOR) vent complex have modified Surtsey's coastal morphology, including the deposition of a 0.5 km-long northern peninsula ( ness ) composed of tephra and rounded lava fragments derived from the southern half of the island. Detailed geomorphologic and sedimentologic mapping of the various surface units now present on Surtsey has been accomplished throughout the history of the evolving island, most recently by Calles et al. (1980) and Ingolfsson (1980). On the basis of these studies, an effort to quantify the topographic characteristics of the primary geomorphic units on the island was initiated by the National Aeronautics and Space Administration (NASA) and the United States Geological Survey (USGS) in 1987. The objective has been to directly measure the microtopographic properties of the widest range of surface types possible, with special emphasis on the pristine or dynamic types. While large-scale topographic maps of Surtsey were prepared in 1968 and 1975 (Norrman, 1980; Norrman and Erlingsson, 1991; Calles et al, 1980), and geodetic leveling surveys have been carried out (Moore, 1980), there have been no recent attempts to geodetically determine the local topography of the island. Because of the rapid rates of geomorphic processes, such as erosion and deposition, on a small, geologically isolated volcanic island such as Surtsey, it is desirable to determine the meter-scale topographic character of its surface units and landforms, and later a remeasurement of the same surfaces to further quantify volumetric change, subsidence, and process rates. In addition, precise measurements of sub-meter-scale topography of pristine geologic surfaces provides necessary data for the investigation of whether various geologic processes demonstrate fractal or self-affine behavior at a range of length-scales within the interval 0.1 in to 1 km. Thus Surtsey offers a unique opportunity to apply new remote sensing techniques to the measurement of the evolving surface "roughness" characteristics of pristine geologic surfaces within an historically well-monitored environment.

Surtsey Research Progress Report↗

USGS2020

Preserving meander bend geometry through scale

Stream meander geometry is a function of hydrologic, geologic, and anthropogenic forces. Meander morphometrics are used in geomorphic classification, ecological characterization, and tectonic and hydrologic change detection. Thus, detailed measurement and classification of meander geometry is imperative to multiscale representation of hydrographic features, which raises important questions. What meander geometries are important to preserve in multi-scale databases? How are geometries measured? How are they preserved? Is the choice between preservation of geometry or use of classification attributes? Questions related to multiscale measurement and representation of hydrographic features continue to emerge with increased spatial and temporal data collection. A key metric for understanding meander bend geometry is sinuosity. The most common measure of sinuosity is the length of a feature divided by the distance between stream head and mouth. The measure relays deviation from a straight line but nothing about meander wavelength. There is not a clear consensus on methods for measuring meander geometry, much less efficiently, at scales made viable with increased data resolution. Here we propose a method for automated characterization of meander wavelength or bend radius. The method, termed Scale-Specific Sinuosity ( S 3 ), is a derivation from the Richardson plot. The Richardson (1961) plot is a classic means of calculating fractal dimension of natural line features and describes feature length (ℓ) given increasing vertex spacing, or step size (S), plotted on a log-log plot. The S 3 metric is defined as negative one times the slope of a Richardson plot for a given stride length. This paper demonstrates utility of S 3 for estimating changes in sinuosity with scale change.

Conference Paper↗

USGS2011

Scaling of flow distance in random self-similar channel networks

Natural river channel networks have been shown in empirical studies to exhibit power-law scaling behavior characteristic of self-similar and self-affine structures. Of particular interest is to describe how the distribution of distance to the outlet changes as a function of network size. In this paper, networks are modeled as random self-similar rooted tree graphs and scaling of distance to the root is studied using methods in stochastic branching theory. In particular, the asymptotic expectation of the width function (number of nodes as a function of distance to the outlet) is derived under conditions on the replacement generators. It is demonstrated further that the branching number describing rate of growth of node distance to the outlet is identical to the length ratio under a Horton-Strahler ordering scheme as order gets large, again under certain restrictions on the generators. These results are discussed in relation to drainage basin allometry and an application to an actual drainage network is presented. ?? World Scientific Publishing Company.

Fractals↗